Decomposition of a multi-state system by series systems

Abstract

In the theory and engineering of reliability, it is one of the important issues for reliability researchers to develop effective evaluation methods of reliability performance of systems. For the case of a binary state system, using the minimal-path or minimal-cut sets of the system, an effective method is given by decomposing a structure function into series or parallel systems. For multi-state systems with partially ordered state spaces, however, sufficient examinations of the decomposition and related subjects have not been given. In this paper, following the definition of a series system of Ohi [28], we show a necessary and sufficient condition for a multi-state system to be a series system, which denotes that a system is series system if and only if the serialisation at system's and component's levels are equivalent with each other, and then presenting the series-decomposition, we show the relationship among the stochastic bounds which is given by the decomposition. Furthermore, some examinations about the pattern of maximal state vectors of a series system are given. In this paper, we omit the discussions about the parallel system, since it is ordered set theoretically dual of the series system.